Consensus ensures that all participants reach a common understanding without relying on a central authority.
For example, Bitcoin uses a consensus algorithms that is called Proof of Work. To prevent double-spending participants (the servers in the Bitcoin network) are required to solve a complex mathematical puzzle.
Another consensus mechanism is called Proof of Stake. This mechanism is also employed to validate and verify transactions, prevent double-spending, and maintain the integrity of the blockchain, however, with this algorithm participants (the servers in the network) have influence based upon the number of tokens staked.
Still another consensus mechanism is the XRP Ledger Consensus Protocol, which as the name suggests is used by the XRP Ledger.
Basically, during the consensus process, participants (servers in the XRP Ledger network) maintain lists of trusted validators and the servers communicate and update proposals until chosen validators agree.